The propagation of a shock wave in a quiescent gas with variable density is investigated. The entropy behind the shock wave is constant. This approach is used by Hunter in the problem of a collapse of an empty cavity. These flows are described by two rather than three partial differential equations with the equation of state of a gas which simplifies the model. In the plane case the enumerable set of algebraic solutions is obtained. Comparison of solutions in the case of constant density and according to Hunter's model for the two problems (about the blast wave and about the converging shock wave) is presented.
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